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Category: Chandra & Satya

  • Satya–Chandra: On Accuracy and Precision

    Chandra:
    Satya, today my measurement matched the true value exactly. So my experiment is perfect, right?

    Satya:
    Not so fast, Chandra. One correct answer can be luck. Tell me—would you get the same result again?

    Chandra:
    Hmm… maybe not. Yesterday it was slightly different.

    Satya:
    Then you may have accuracy, but not precision.

    Chandra:
    So accuracy is closeness to truth, and precision is consistency?

    Satya:
    Exactly.
    Accuracy asks, “How close am I to reality?”
    Precision asks, “How reliable am I?”

    Chandra:
    Satya, suppose an examiner evaluates a student’s answer.
    The student’s true understanding deserves 6 marks.

    Satya:
    Good. Now tell me—how does the examiner mark?

    Chandra:
    In one case, the examiner gives 8, 8, 8, 8 every time.

    Satya (raises an eyebrow):
    Then the examiner is consistent… but biased.

    Chandra:
    So the marking is precise, but not accurate?

    Satya:
    Exactly.
    Precision reflects the examiner’s habit.
    Accuracy reflects the examiner’s judgement.

    Chandra:
    What if the examiner gives 6, 6, 6, 6?

    Satya (smiles):
    Then consistency meets truth.
    Both precision and accuracy are achieved.

    Chandra:
    And if the marks are 8, 4, 9, 3?

    Satya:
    Then the examiner sometimes hits the truth, sometimes misses it.
    Accurate on average, but lacking precision.

    Chandra (thinking):
    So repetition alone doesn’t guarantee fairness.

    Satya:
    No.
    Without accuracy, precision becomes reliable error.
    Without precision, accuracy becomes fortunate coincidence.
    And remember—without precision, accuracy cannot be trusted;
    without accuracy, precision is meaningless.

    Chandra:
    That sounds like life advice too.

    Satya (laughs):
    Physics always is.

  • Dimensional Reasoning

    Satya:

    Chandra…I forgot the formula for the period of a pendulum.

    Chandra:

    Forgetting formulas is normal.

    Satya:

     I remember something 2\pi …. g …..l… umm…but not exactly

    Chandra:

     Then don’t memorize the formula. Let dimensions guide you.

    Satya:

    Dimensions? How?

    Chandra:

    The period is time period. Time has dimension of [T], length has [L], and g has [L][T]-2. Now combine them so that the final result has dimension [T].

    Satya:

     I got it

    T \propto \sqrt{\frac{l}{g}}

    Chandra:

    Exactly. No memorization, just logic.

    Satya:

     Wow.. so I can rebuild and verify formulas!

    Chandra:

     Correct. Now tell me quickly,

    v=u+at^2

    right?

    Satya: Yeah.. ahh.. wait a minute

              Nooo! My brain memorized, but dimensions caught the error.

    v and u are [L][T]-1 ,

    a t^{2} is [L]

    Therefore It must be

    v=u+at

    Now I got a spell check for equation.